When Under Armour signed a 10-year agreement to put its name on the Baltimore Ravens’ practice facility in 2012, the company and the team envisioned a link between two hip brands.

Steve Bisciotti, the Ravens’ owner, spoke that day about how he and Kevin Plank, Under Armour’s chief executive, were “two young guys fighting some very established competitors.”

On Monday, Bisciotti sat in the auditorium of the Under Armour Performance Center in Owings Mills, Md., in front of a backdrop emblazoned with the logos of the company and the team, standard stage management in sports when coaches, players and team officials speak to the news media.

But this was not the sort of event that a sponsor cherishes. Bisciotti was holding a news conference to rebut a report by ESPN that the Ravens had lobbied the N.F.L. for lenience in punishing running back Ray Rice after he was arrested and charged with assaulting Janay Palmer, then his fiancée, in February.

This month, after a video showed Rice punching Palmer, who married him a day after the indictment was issued, he was cut by the Ravens and suspended indefinitely by the league.

On Tuesday, Under Armour issued a statement saying that the Ravens had “made a mistake” in how they dealt with Rice after the initial accusation and that “they have learned hard lessons and vowed to implement a policy to ensure it doesn’t happen again.” The company’s statement added: “We believe they will work through this and find ways to have a positive societal impact in efforts to stem domestic violence.”

It was the latest illustration of the difficulties faced by sponsors as the N.F.L. struggles to deal with its mishandling of several recent cases of domestic violence involving players. Some sponsors have issued statements, a few tougher than others, but their top executives have been loath to speak publicly, either to chastise or to support the league.

Lowell McAdam, the chairman of Verizon Communications, wrote on his LinkedIn page that because of the company’s deep involvement in programs to prevent domestic violence, “we can be far more effective in preventing domestic violence in the arena with our partners at the N.F.L., rather than backing away from the controversy.”

So far, no sponsor has pulled out of its deal, although Radisson Hotels suspended its sponsorship with the Minnesota Vikings after running back Adrian Peterson was accused of child abuse, and Crest, a Procter & Gamble brand, dropped its sponsorship from the league’s breast cancer awareness program.

While distancing themselves from the domestic violence cases, sponsors do not want to dissociate themselves from the N.F.L., a singularly powerful marketing outlet. If they speak out too forcefully against the league, sponsors could hurt the league when it is down. They could also hurt themselves because of an association they have built over time. The only way that sponsors will change their approach to the crisis, marketing executives said, is if they see a drastic drop-off in their sales or the value of the league’s brand.

“Either way, it is all about protecting your business,” said Tony Ponturo, a former vice president for global media at Anheuser-Busch, one of the league’s biggest sponsors. (Anheuser-Busch released a statement last week that said it was “disappointed and increasingly concerned by the recent incidents that have overshadowed this N.F.L. season.”)

Consumer perception of the N.F.L. has, at least for now, plunged to its lowest level in more than two years, according to YouGov BrandIndex, a research service. A score of -100 to 100 was calculated based on interviews with 10,000 people who were asked, “If you’ve heard anything about the brand in the last two weeks, through advertising, news or word of mouth, was it positive or negative?”

After peaking this year on Sept. 8 with a 36, the N.F.L.’s score on Sept. 22 had plunged to a -42, with men giving the league a -46 and women a -38.

The last time the league endured such a drastic dip in perception, according to YouGov, was in June 2012, when the score dipped to a -26 in the midst of the New Orleans Saints bounty scandal and the filing of a consolidated complaint by former players accusing the N.F.L. of hiding information linked to football-related head trauma.

Sponsors stick with the N.F.L. for years, not weeks, because its game broadcasts attract mass audiences that cross the boundaries of age, race and gender. They sign multiyear deals that often form the foundation of lengthy consumer marketing campaigns, while also agreeing to spend money on televised advertising during games. Allen Adamson, chairman of the North American region of Landor Associates, a branding consulting firm, said: “The N.F.L. is the only game in town. It is not like they can take their sponsorship and marketing dollars to baseball or Ping-Pong.”

Sponsorships for the league and teams were valued by IEG, a sponsorship research and consulting company, at $1.07 billion in 2013. Total advertising spending on N.F.L. broadcasts reached $4 billion in 2013, up 10 percent over the previous year, according to WPP’s Kantar Media, an ad tracking firm. The top advertiser in 2013 was Anheuser-Busch, with spending of $185.3 million.

Cutting their ties to the N.F.L. — or even temporarily pulling ads or distancing a brand from the league — is not likely to happen since it can have ramifications for a company’s broader strategy.

Michael Lynch, a former head of global sponsorship marketing at Visa USA who now runs the United States consulting practice at Repucom, a sports marketing research firm, said, “If a sponsor pulls out, they may be hard-pressed to get back in when the issue has been resolved to their satisfaction.”

“At this point, a lot already has gone out the door,” Ponturo said, noting that about half of the sponsorship money already has been spent on laying the infrastructure of the sponsorship.

Marketing executives said that they typically were put on alert as soon as news about a controversy breaks and monitor how the partner handles the scandal. They are forced to respond when the issue continues to build and they face pressure from consumers, stockholders and employees. In the current N.F.L. crisis, brands are particularly sensitive to how the issue is playing out among women.

“You start getting dragged into the conversation even if you did nothing wrong,” Ponturo said. “You could be threatened with boycotts now of one of your products.”

In these situations, sponsors typically call one another to make sure that their statements are similar and also run the statement by the leagues or teams, the executives said.

“Sponsors are expecting their partners to do the right thing,” Lynch said. “And if they don’t, then morals clauses kick in and they have to consider the alternatives.”

A version of this article appears in print on , on Page B12 of the New York edition with the headline: Sponsors Walk Fine Line When a Powerful Marketing Partner Is in Crisis. Order Reprints | Today’s Paper | Subscribe